You'll need to add all the CRS/AMS to the water in your HLT to get the alkalinity down to the right value.

When you add the gypsum depends on how much calcium you already have in your water. If it's 100ppm or above then the gypsum can be sprinkled on top of the grains after the mash but before the sparge. Some would say half at the beginning and then the other half later on.

It's also worth thinking about the alkalinity of your sparge water. I always add a further 2.5 ml of CRS/AMS to the liquor in the HLT after I've run the amount needed for the mash into the mash tun. In my case, this brings the alkalinity of the sparge liquor down by about another 10 ppm.

Do the chemicals go into the mash water all at once or should they be divided between the mash water and the sparge water?

The mash and sparge stages do have their own ideals, so ideally they would be treated separately. The difference may be less with very pale beers, but particularly with darker grains the mash liquor's alkalinity would typically be quite lot higher than is preferred for sparging.

I will aim for the mash liquor's alkalinity to end up with the desired mash pH (typically ph 5.4-5.8 at room temperature), this can mean a liquor alkalinity of anything between 20ppm and 150ppm according to the grain types involved. But I'll adjust the sparge liquor's alkalinity to be quite modest (say around 15ppm). Normally this will be done via the acids (in your case CRS) but in some cases it can help me to move the salt additions around too - such as if struggling to get the mash-liquor's alkalinity high enough for a dark beer.

For the salt additions otherwise, there seem to be proponents of most combinations for splitting them between mash, sparge and direct to the boil - I'd be interested to hear what others have to say about this. My own preference is to have most of the salts in the mash and sparge, unless as mentioned some are moved to help achieve alkalinity or ph targets. But the mash will retain/lose quite a lot of them so I always start out with healthy amounts of calcium in particular.

Talking of which, the gypsum you mention will dissolve in the liquor for most people with a bit of stirring (in the main volume anyway, don't fall into the trap of trying to dissolve it in a small amount of water first), if that is so then you have the choice of either doing that or adding to the grain. But it isn't so easy to dissolve for some people, with their water or quantities needed, so as others have mentioned adding to the grain could be preferred in that case.

BTW, I would suggest (if you haven't already) getting Salifert's alkalinity and calcium test kits, rather than relying on supplier's reports. These are generally averaged figures and especially if the water varies much it could be quite different on brew day. The kits will also allow you to check that liquor additions have had the intended result.

Liquids in the liquor, salts in the grain. Some salts aren’t fully dissolvable so they’ll be left behind in the HLT

The only salt commonly used in brewing that doesn't dissolve well, is chalk. All the rest of them easily dissolve...however you will have to stir the water. If you dump them into the HLT and expect them to dissolve on their own, you will be disappointed. STIR!!

Be aware that when you add your minerals and acids does have an effect on mashing pH. Using software to assess the effect of mash and/or kettle additions, is a good idea.

One generally waits 10 minutes before taking pH measurements of the mash and then corrects it (with lactic acid, that is liquid). If you want to include the effects of salts you have to add them before that. So salts at mashing in, lactic a bit later and maybe again in the copper.

One generally waits 10 minutes before taking pH measurements of the mash and then corrects it (with lactic acid, that is liquid). If you want to include the effects of salts you have to add them before that. So salts at mashing in, lactic a bit later and maybe again in the copper.

ingo

One generally does not do this

One normally takes a reading of alkalinity using a test kit, then one determines the amount of acids (hydrochloric and/or sulphuric) required to reduce the alkalinity to where one wants it to be, then one waits 15 minutes after mashing in to check the pH. If the pH is not in the range 5.3 to 5.6/7 then one makes a note of it and the next time that grist is used, one uses more or less acids as required depending on the alkalinity at the time of brewing.

It really is pointless trying to chase mash pH, as it will be too high, you add acid it drops too low, you add chalk, it goes too high ... and round and round.

I would never use lactic acid, it's not normally found in beer (except traditionally in Berliner weiss, and at very low levels in triple decocted beers), and has quite a low taste threshold ... I can detect it in the final beer at 6ml per 50L of liquor!!

Several reasons. Water isn't a constant, there are two constantly changing supply sources here.
Some of the malts I use are sour, really sour and not constant (not the German sour malts (with lactic acid)) These are partly fermented with lacobacillus, think sour melanoidin/aromatic malts.

First thing I do is get the Ca++ content op to ~70 ppm (excluding what's in the malts) using CaCl2, based on the suppliers monthly averages in the water report.

Then I concentrate on a mash pH in the range 5.2-5.5 and 5.2 after the boil. Pre calculate it based on AJ deLange's material and measure and correct only once. Works just fine for me. Could use phosphoric acid, or any other 'tasteless' one, been using lactic acid ever since.
Lactic acid in beer, not counting sour beers, comes not from the yeast but from malting, nowadays in small amounts.

The main thing is doing it always the same way, the 'absolute' process is not that important. So, don't keep correcting, don't keep measuring, always measure at the same time.

Regarding availability of chemicals, there's a 'grow shop' around the corner.

One generally waits 10 minutes before taking pH measurements of the mash and then corrects it (with lactic acid, that is liquid). If you want to include the effects of salts you have to add them before that. So salts at mashing in, lactic a bit later and maybe again in the copper.

ingo

I wouldn’t do that at all - it’s not too difficult to calculate where you should be pH wise - if your pH is out after 10 minutes of mashing, it ain’t right! Same goes for temperature. Most of the activity in a mash happens in the first 15 mins or so.